Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777846 | Topology and its Applications | 2017 | 15 Pages |
Abstract
In this paper, we introduce the notion of a partially (para)topological group, using generalized topology in the sense of H. Delfs and M. Knebusch. We study some basic properties of this kind of structures. Among them, we prove that an important theorem of Banakh and Ravsky, applied to their proof in ZFC that every regular paratopological group is completely regular, can be false in a model for ZF. Therefore, it is an open problem whether there exists a model for ZF in which a Hausdorff topological group need not be completely regular. We notice that Banakh-Ravsky theorem that every regular paratopological group is completely regular is provable in every model for ZF+DC.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Cenap Ãzel, Artur PiÄkosz, Mohammed Al Shumrani, Eliza Wajch,